Method and apparatus for measuring a local acceleration of gravity

ABSTRACT

An apparatus and method for measuring a local acceleration of gravity includes releasing a ferrous rod having a regular alternating pattern of reflective and non-reflective portions on a surface thereof from an electromagnetic holder so that the rod falls with a substantially vertical acceleration and substantially no angular velocity about a center of mass of the rod. The falling rod is illuminated with a light emitting diode (LED) configured to emit infrared (IR) light, and IR light emitted by the LED and reflected by the falling rod is detected with a photodiode. A two-state signal is generated corresponding to an illumination state of the photodiode by the reflected IR light. Times of transitions between the two states in the generated signal are calculated to determine kinematic data, and the kinematic data is fitted to a predetermined curve to calculate a local acceleration of gravity.

BACKGROUND

Field of the Disclosure

The present disclosure relates to methods and apparatus for measuringlinear acceleration, and more specifically relates to methods andapparatus for measuring a local acceleration of gravity.

Description of the Related Art

Since the beginning of human civilization, many theories, hypotheses,and experiments were proposed to understand the dynamics of fallingobjects. The Greek philosopher Aristotle suggested that objects fall atspeeds proportional to their masses. Aristotle's incorrect theory wasdiscredited by Galileo's landmark experiment, where according to legend,Galileo dropped balls of different densities and masses from the towerof Pisa. Galileo noticed that if released simultaneously from rest, allobjects tend to land at the same time, concluding that time of fall isindependent of the mass of the object.

In the last few decades, and as a result of many advancements in scienceand technology, many techniques have been proposed to provide veryprecise and accurate measurement of the acceleration due to gravity. Thebasis of techniques used to measure acceleration due to gravity variesfrom using conventional mechanical methods, to manipulating cold atoms,to employing atomic interferometers. Although most of the aforementionedtechniques can yield very accurate and precise measurement of theacceleration due to gravity, when using these techniques in introductoryphysics laboratory there are a few shortcomings.

This is due to the fact that these techniques require expensiveexperimental setups involving many components. Additionally, thesetechniques are difficult to perform and require near-ideal conditions toobtain reliable results. Last, but not the least, these techniquesnecessitate the hiring of highly-trained personnel. All theselimitations can make the employment of these advanced techniques inteaching laboratories a difficult endeavor. The measurement of theacceleration due to gravity is now a standard teaching experiment inmany introductory physics laboratory courses. Thus, most physics studentlabs desire an approach to measuring the acceleration due to gravity byusing a method that is economical, simple, and safe, and which can alsoyield a reasonable value of a local acceleration of gravity g.

Of the many simple techniques employed to measure acceleration due togravity in standard physics books, the period of a pendulum'soscillation and the time of fall of an object as a function of heightare the most commonly used methods. While the pendulum method can yielda relatively wide range of variation in the value of g due to effect ofair resistance and other systematic errors, the latter method can alsobe very sensitive to imprecise measurements of times and heights offall, consequently, causing significant variation in determining thevalue of g. In the last few decades, many experimental techniques havebeen proposed to replace these two simple methods to evaluate g.However, the application of these techniques was either deemed expensiveor inaccurate, and sometimes unsafe.

SUMMARY

One embodiment of the invention is drawn to an apparatus for measuring alocal acceleration of gravity. The apparatus includes an electromagneticholder configured to releasably hold a ferrous rod having a regularalternating pattern of reflective and non-reflective portions on itssurface. An infrared (IR) transceiver includes a light emitting diode(LED) configured to emit IR light, and a photodiode configured to detectIR light emitted by the LED which is reflected off the ferrous rod backto the IR transceiver. An output circuit of the IR transceiver outputs atwo-state signal corresponding to an illumination state of thephotodiode by the reflected IR light. A power supply is configured tothe power the electromagnetic holder and the IR transceiver.

A controller is configured to control a current from the power supply tothe electromagnetic holder to the cause electromagnetic holder torelease the rod, cause the IR transceiver to emit IR light, receive thesignal from the IR transceiver, and calculate times of transitionsbetween the two states in the received signal to determine kinematicdata. The controller calculates a local acceleration of gravity from afit to the kinematic data.

Another embodiment of the invention is drawn to a method for measuring alocal acceleration of gravity. The method includes releasing an objecthaving a regular alternating pattern of reflective and non-reflectiveportions on a surface thereof from an electromagnetic holder so that theobject falls with a substantially vertical acceleration andsubstantially no angular velocity about a center of mass of the object.The method also includes illuminating the falling object with a lightemitting diode (LED) configured to emit infrared (IR) light, anddetecting IR light emitted by the LED and reflected by the fallingobject with a photodiode configured to detect IR light emitted by theLED and reflected by the falling object

A two-state signal is generated based on the detecting. The two-statesignal corresponds to an illumination state of the photodiode by thereflected IR light. Times of transitions between the two states in thegenerated signal are calculated to determine kinematic data, and thekinematic data is fitted to a predetermined curve. A local accelerationof gravity is calculated from the fitting.

Another embodiment of the invention is drawn to a non-transitorycomputer-readable medium storing a program thereon for causing acomputer to perform a method for measuring a local acceleration ofgravity. The method includes releasing an object having a regularalternating pattern of reflective and non-reflective portions on asurface thereof from an electromagnetic holder so that the object fallswith a substantially vertical acceleration and substantially no angularvelocity about a center of mass of the object. The method also includesilluminating the falling object with a light emitting diode (LED)configured to emit infrared (IR) light, and detecting IR light emittedby the LED and reflected by the falling object with a photodiodeconfigured to detect IR light emitted by the LED and reflected by thefalling object.

A two-state signal is generated based on the detecting. The two-statesignal corresponds to an illumination state of the photodiode by thereflected IR light. Times of transitions between the two states in thegenerated signal are calculated to determine kinematic data, and thekinematic data is fitted to a predetermined curve. A local accelerationof gravity is calculated from the fitting.

BRIEF DESCRIPTION OF THE DRAWINGS

A more complete appreciation of the disclosed embodiments and theattendant advantages thereof will be more readily obtained by referenceto the accompanying drawings when considered in connection withfollowing detailed description.

FIG. 1 illustrates an exemplary embodiment of an apparatus for measuringa local acceleration of gravity.

FIG. 2 illustrates variation in rod geometry and reflectance.

FIG. 3 illustrates an exemplary output of the IR transceiver.

FIG. 4 illustrates an exemplary embodiment of an apparatus for measuringa local acceleration of gravity.

FIG. 5 illustrates an exemplary controller in an apparatus for measuringa local acceleration of gravity according to an aspect of thedisclosure.

FIG. 6 is a flowchart illustrating an exemplary embodiment of a methodfor measuring a local acceleration of gravity.

FIG. 7 illustrates an exemplary curve fit of data to show the localacceleration of gravity in an aspect of the disclosure.

DETAILED DESCRIPTION

The following descriptions are meant to further clarify the presentdisclosure by giving specific examples and embodiments of thedisclosure. These embodiments are meant to be illustrative rather thanexhaustive. The full scope of the disclosure is not limited to anyparticular embodiment disclosed in this specification, but rather isdefined by the claims.

One embodiment of the invention is drawn to an apparatus for measuring alocal acceleration of gravity. The apparatus includes an electromagneticholder configured to releasably hold a ferrous rod having a regularalternating pattern of reflective and non-reflective portions on itssurface. An infrared (IR) transceiver includes a light emitting diode(LED) configured to emit IR light, and a photodiode configured to detectIR light emitted by the LED which is reflected off the ferrous rod backto the IR transceiver. An output circuit of the IR transceiver outputs atwo-state signal corresponding to an illumination state of thephotodiode by the reflected IR light.

A power supply is configured to the power the electromagnetic holder andthe IR transceiver. A controller is configured to control a current fromthe power supply to the electromagnetic holder to the causeelectromagnetic holder to release the rod, cause the IR transceiver toemit IR light, receive the signal from the IR transceiver, and calculatetimes of transitions between the two states in the received signal todetermine kinematic data. The controller calculates a local accelerationof gravity from a fit to the kinematic data.

In an aspect of the invention, the apparatus includes the ferrous rodhaving the regular alternating pattern of reflective and non-reflectiveportions on the surface thereof.

In an aspect of the invention, the rod has a substantially cylindricalshape.

In an aspect of the invention, the alternating pattern is formed atregular intervals of 1 centimeter.

In an aspect of the invention, the alternating pattern is formed byetching a surface of the rod.

In an aspect of the invention, the alternating pattern is formed byapplying a black resin, epoxy, or paint to a surface of the ferrous rod.

In an aspect of the invention, transitions between the reflectiveportions and the non-reflective portions of the alternating pattern areblurred by varying a concentration of an IR absorber in the black resin,epoxy, or paint in a portion of the alternating pattern at thetransition.

In an aspect of the invention, the surface of the rod is shaped in apattern corresponding to the reflective portions and the non-reflectiveportions of the rod.

In an aspect of the invention, the surface of the rod is shaped in aconcave pattern corresponding to the reflective portions and thenon-reflective portions of the rod.

In an aspect of the invention, the surface of the rod is shaped in aconcave pattern corresponding to the reflective portions and thenon-reflective portions of the rod.

In an aspect of the invention, the alternating pattern is formed byapplying a black resin, epoxy, or paint to a surface of the ferrous rod.In an aspect of the invention, the alternating pattern is formed byprinting a black and white pattern on paper and fixing the paper to theferrous rod.

Another embodiment of the invention is drawn to a method for measuring alocal acceleration of gravity. The method includes releasing an objecthaving a regular alternating pattern of reflective and non-reflectiveportions on a surface thereof from an electromagnetic holder so that theobject falls with a substantially vertical acceleration andsubstantially no angular velocity about a center of mass of the object.The method also includes illuminating the falling object with a lightemitting diode (LED) configured to emit infrared (IR) light, anddetecting IR light emitted by the LED and reflected by the falling rodwith a photodiode configured to detect IR light emitted by the LED andreflected by the falling object.

A two-state signal is generated based on the detecting. The two-statesignal corresponds to an illumination state of the photodiode by thereflected IR light. Times of transitions between the two states in thegenerated signal are calculated to determine kinematic data, and thekinematic data is fitted to a predetermined curve. A local accelerationof gravity is calculated from the fitting.

In an aspect of the invention, the method further includes a secondreleasing of the object having the regular alternating pattern ofreflective and non-reflective portions on the surface thereof from theelectromagnetic holder so that the object falls with a substantiallyvertical acceleration and substantially no angular velocity about thecenter of mass of the object, and a second illuminating of the fallingobject with a light emitting diode (LED) configured to emit infrared(IR) light. A second detecting of IR light emitted by the LED andreflected by the falling object with a photodiode configured to detectIR light emitted by the LED and reflected by the falling object isperformed, and a second generating a two-state signal based on thedetecting, the two-state signal corresponding to an illumination stateof the photodiode by the reflected IR light.

A second calculating times of transitions between the two states in thegenerated signal is performed to determine kinematic data for the secondreleasing. The fitting the kinematic data to the predetermined curveincludes the kinematic data from the first calculating and the kinematicdata from the second calculating.

Another embodiment of the invention is drawn to a non-transitorycomputer-readable medium storing a program thereon for causing acomputer to perform a method for measuring a local acceleration ofgravity. The method includes releasing a ferrous rod having a regularalternating pattern of reflective and non-reflective portions on asurface thereof from an electromagnetic holder so that the rod fallswith a substantially vertical acceleration and substantially no angularvelocity about a center of mass of the rod. The method also includesilluminating the falling rod with a light emitting diode (LED)configured to emit infrared (IR) light, and detecting IR light emittedby the LED and reflected by the falling rod with a photodiode configuredto detect IR light emitted by the LED and reflected by the falling rod.

A two-state signal is generated based on the detecting. The two-statesignal corresponds to an illumination state of the photodiode by thereflected IR light. Times of transitions between the two states in thegenerated signal are calculated to determine kinematic data, and thekinematic data is fitted to a predetermined curve. A local accelerationof gravity is calculated from the fitting.

FIG. 1 illustrates an exemplary embodiment of an apparatus 100 formeasuring a local acceleration of gravity. The apparatus 100 has anelectromagnet 140 mounted on a vertical beam 190 to achieve free-fallrelease of an object. A height of the beam 190 should be chosen so thatthe object released does not contact the floor until after required datahas been recorded, i.e., more than twice a length of the object.However, height in excess of 2 meters may make the apparatus moredifficult for students to work with, especially young students. Forexample, the height of the beam could be 2.1 meters for an object havinga length of 1.0 meter. Preferably, the beam 190 is 2.0 meters in heightor less, and more preferably 1.5 meters in height or less.

The falling object can be a ferrous rod 170. Alternatively, the rod 170may be of a ferromagnetic non-ferrous material, such as nickel, cobalt,or the like, such that the rod 170 can be held by the electromagnet 140.The rod 170 is marked with a regular alternating pattern of reflectiveand non-reflective portions. The pattern is configured on a surfaceportion of the rod. The pattern may extend around an entirety of thecircumference of the rod, but this is not required. The regularalternating pattern preferably has a constant pitch, with the reflectiveand non-reflective portions having equal length. A pitch of the regularpattern is preferably between 1 cm per pair and 5 cm per pair, and morepreferably is 2 cm per pair, with the reflective portion and thenon-reflective portion of the 2 cm pair each being 1 cm in length. Amodulation of reflected IR light produced by the alternating pattern ofreflective and non-reflective portions will be used to determine thekinematics of the falling rod 170, and thus a local acceleration ofgravity. A number of transitions between reflective and non-reflectiveportions of the rod 170 will determine a number of data pointsgenerated.

The rod 170 may have any cross-sectional shape, but is elongated so asto allow the regular alternating pattern of reflective andnon-reflective portions. The rod 170 should be long enough relative to alength of the reflective and non-reflective portions in the regularalternating pattern that a substantial number of data points willgenerated for fitting to a quadratic curve. The rod 170 should also beheavy enough and sized so that the effects of air resistance will benegligible during the operation of the apparatus. The rod 170 ispreferably less than 1 meter in length, and more preferably less thanhalf a meter in length. Preferably, the rod 170 has a cylindrical shape,and preferably the rod 170 has a radius of 0.02 m or less, and morepreferably 0.01 m or less. Preferably, a mass of the rod is between 0.1kg and 1 kg, and more preferably between 0.1 kg and 0.5 kg. For example,a 0.13 kg cylindrical homogenous rod of 0.01 m radius and 0.19 m lengthwith a metallic tip to establish contact with the electromagnet could beused.

The regular alternating pattern of reflective portions 171 andnon-reflective portions 172 can be formed on or fixed to a surface ofthe rod 170 in a number of ways available to one of ordinary skill inthe art. For example, a paper of 0.01 m equal-width white and blackstripes, printed, for example, using a laser printer, can be wrapped onthe rod 170. The regular alternating pattern can also be marked on therod, for example, by applying a black resin, epoxy, or paint to the rod170 to form the non-reflective portions. The black resin, epoxy, orpaint can include, for example, charcoal, black iron oxide, and thelike, to absorb the IR light. The reflective portions of the rod can beformed by a natural metallic surface of the rod, a chemical ormechanical polishing of the surface of the rod, or by applying an IRreflective resin, epoxy, or paint to the rod 170. The IR reflectiveresin, epoxy, or paint can include, for example, zinc oxide, titaniumdioxide, and the like, to reflect the IR light. Especially in the nearIR and short wave IR, that is, wavelengths from 0.8 microns to 3microns, resins, epoxies, and paints which are white, or reflective, inthe visible spectrum are frequently white, or reflective, in the near IRand short wave IR, and resins, epoxies, and paints which are black, ornon-reflective, in the visible spectrum are frequently black, ornon-reflective, in the near IR and short wave IR. Alternatively, aregular alternating pattern of different reflectivities can be etchedonto the surface of the rod.

The reflective portions 171 and the non-reflective portions 172described above are configured to each have a uniform reflectance value,the reflective portions 171 having a high reflectance and thenon-reflective portions 172 having a low reflectance, with thetransition between the two reflectance values being as sharp as possibleso as to produce the best data. This results in a reflected IR signalwhich resembles a square wave, i.e., having sharp transitions. However,the rod 170 may also be configured so that the transitions are lesssharp. This provides variation in the data, introducing a known “noise”or error in the data, which can be used as an additional resource forinstruction regarding measurement error in a classroom environment.

For example, as shown in FIG. 2, the transitions can be made less sharpby varying the reflectance of the reflective portions 171 a and thenon-reflective portions 172 a gradually at an interface between theportions. The ellipses indicate portions of the rod 170 omitted from thedrawing. In an embodiment where the non-reflective portions 172 areformed by marking the rod 170 with a black resin, epoxy, or paint, theIR absorbing material in the resin, epoxy, or paint may be varied overan area of 1 mm or 2 mm in width, for example, resulting in transitionsbetween the reflective portions and non-reflective portions which arenot sharp as in a square wave, but spread out as in a trapezoid wave orother waveform. In an embodiment where the non-reflective portions 172are formed by etching the rod 170, the etching could be transitionedvaried over an area of 1 mm or 2 mm in width, for example, between noetching and full etching, resulting in transitions between thereflective portions and non-reflective portions which are not sharp asin a square wave.

In another example, the transitions can be made less sharp by varyingnot the reflectance values of the reflective portions 171 and thenon-reflective portions 172, but rather a geometry of the surface of therod 170 having the reflective portions 171 and the non-reflectiveportions 172. A non-uniformity or irregularity in the geometry of thesurface of the rod 170, for example, having convex surfaces on thereflective portions 171 b and non-reflective portions 172 b, concavesurfaces on the reflective portions 171 c and non-reflective portions172 c, or otherwise irregular surfaces on the reflective portions 171 dand non-reflective portions 172 d, can also result in transitionsbetween the reflective portions and non-reflective portions which arenot sharp as in a square wave, but spread out as in a trapezoid wave orother waveform.

All the types of transitions indicated above can be incorporated on therod 170, as shown in FIG. 2, either individually or in combination, soas to produce a data set having portions with relatively little error(for the portion of the rod with the sharply divided reflective portions171 and non-reflective portions 172), as well as portions in which asystematic error is introduced by reflective portions 171 a, 171 b, 171c, and 171 d, non-reflective portions 172 a, 172 b, 172 c, and 172 d,and the corresponding variable transitions between reflective portionsand non-reflective portions. The regular alternating pattern ofreflective and non-reflective portions can also be configured to have asharpness of the transitions which decreases along a the length of therod.

An IR transceiver 130 is disposed below and to a side of a position ofthe rod 170 when held by the electromagnet 140. The IR transceiver 130is preferably not more than 5 cm below an end of the rod 170, and morepreferably not more than 2 cm below the end of the rod 170. The IRtransceiver 130 is configured with an IR light emitting diode (LED) 132and an IR photodiode 134 which is sensitive to the wavelengths of IRlight emitted by the IR LED 132. The IR LED 132 is preferably anamorphous silicon (a-Si) diode, a silicon (Si) diode, or an indiumgallium arsenide (InGaAs) diode. The IR LED 132 emits IR light havingwavelengths preferably between 0.8 microns and 5 microns, and morepreferably between 0.8 microns and 2.5 microns. The IR LED 132 emitslight which does not directly illuminate the IR photodiode 134 butrather, after the electromagnet 140 releases the rod 170, indirectlyilluminates the IR photodiode 134 via reflected light from the fallingrod 170. The pattern of the reflected light is modulated by the regularalternating pattern of reflective portions 171 and non-reflectiveportions 172 of the rod 170.

The IR LED 132 and the IR photodiode 134 are disposed at a same heightand in proximity to one another, and near a path of the rod 170 afterits release from the electromagnet 140. For example, the IR LED 132 andthe IR photodiode 134 can be separated in the IR transceiver 130 by a 3mm horizontal distance, and can be positioned horizontally to point in asame direction. The IR LED 132 and the IR photodiode 134 are disposednear the path of the falling rod 170 in order to have a strong reflectedreturn of the IR light from the rod, preferably within 10 cm of the pathof the falling rod, and more preferably within 5 cm of the path of thefalling rod.

An output circuit of the IR transceiver 130 outputs a signal which is anon-periodic two-state rectangular wave, for example, at the 5 Volt (V)and 0 V levels, corresponding to illuminated and non-illuminated states,respectively, of the IR photodiode 132. A digital oscilloscope 180 isset to a capture mode and is used to record and observe the outputsignal at a high resolution. For example, the sampling rate of thesignal output from the IR transceiver 130 by the digital oscilloscope180 could be 100K samples per second or higher.

The IR transceiver 130 is connected to a DC power supply 150, forexample, of 5 V and 1 Amp (A), and is placed in close proximity to thelower end of the rod 170 as well as to the falling rod's trajectory inorder to optimize the reflected signal received. The DC power supply 150also provides the current for the electromagnet 140.

The rod 170 is attached to the electromagnet 140 and is held still forfew seconds to ensure that the fall will be perfectly vertical. Toensure vertical free falling, a leveling of the electromagnet can beverified, for example, with a spirit level. Also, when utilizing theapparatus 100, air conditioning units or fans in the vicinity of theapparatus 100 can be turned off in order to eliminate a possible effectof air streams that could influence the free-fall conditions of theobject, and incandescent lights or other sources of interfering IRillumination in the vicinity of the apparatus 100 can be extinguishedbefore use.

When the electromagnet 140 is switched off, the rod 170 is released fromrest. Emitted IR light from the IR LED 132 is reflected by the rod 170as it falls past the IR transceiver 130, and received by the IRphotodiode 134. As a result, a non-periodic rectangular wave will berecorded. The distinct 5 V peaks correspond to the reflected signalreceived by the IR photodiode while a reflective portion 171 of the rod170 is being illuminated by IR LED 132. The 0 V valleys correspond tothe reflected signal received by the IR photodiode while anon-reflective portion 172 of the rod 170 is being illuminated by IR LED132.

FIG. 3 illustrates an exemplary output of the IR transceiver. FIG. 3shows a signal output by the IR transceiver 130 (in volts) versuselapsed time (in seconds) for 19 total stripes (10 white and 9 black),each stripe having a fixed 0.01 m width. A technique used to determinethe corresponding beginning or end time of either the white or blackstripes is as follows. The beginning time of each white stripe isdetermined to be the start of the rise of the peak, and the ending timeof the white stripe is determined to be the beginning of the fall of thepeak. The beginning time of the black stripes is determined to be thebeginning of the fall of the peak, and the end of the black stripe isdetermined to be the start of the rise of the following peak.

An observed trend of the width of the peaks is to decrease as a functionof elapsed time. This trend is expected as the width of each peakcorresponds to the time of fall of that stripe. The widest peak (0.0254s), to the left in FIG. 3, corresponds to time of fall of the firstwhite stripe at the lower end of the falling rod 170, whereas, thenarrowest peak (0.0055 s), to the right in FIG. 3, corresponds to thefall time of the top white stripe of the falling rod 170. Since thewidth of each stripe is fixed at 0.01 m, from FIG. 3 it is clear thatduring the fall the lower end of the rod 170 passed the IR transceiver130 with lower speed than the upper end of the rod 170. In other words,the free falling rod 170 is experiencing an acceleration due only togravity, which causes the observed increase in its speed as the rodfalls.

FIG. 4 illustrates a second exemplary embodiment of an apparatus 200 formeasuring a local acceleration of gravity. Like elements of theapparatus 200 to the apparatus 100 are given a same number, and are notdescribed again.

In the embodiment of FIG. 4, a controller 105 is configured to operatethe apparatus 200. The controller 105 performs the functions of thedigital oscilloscope 180, including receiving the output signal sentfrom the IR transceiver 130 via the output circuit 136. Additionally,the controller is able to start and stop emission of IR light by the IRLED 132 in the IR transceiver 130. The IR LED 132 and the IR photodiode134 lie one behind the other from the perspective of FIG. 4, at the sameheight.

The controller 105 is also electrically connected to a switch 160, so asto be able to cause the switch 160 to open and close. Theelectromagnetic 140 is connected to the DC power supply 150 through theswitch 160. When the controller 105 opens the switch 160, current doesnot flow to the electromagnet 140, and the rod 170 is released by theelectromagnet. When the controller 105 closes the switch 160, theelectromagnet 105 generates a magnetic field, and will hold the ferrousrod 170.

FIG. 5 illustrates exemplary controller 105 in the apparatus 200 formeasuring a local acceleration of gravity according to an aspect of thedisclosure. In FIG. 4, the controller 105 includes a processor 101 whichperforms the processes described above and below. The process data andinstructions may be stored in memory 102. These processes andinstructions may also be stored on a storage medium disk 104 such as ahard drive (HDD) or a portable storage medium, or may be storedremotely. Further, the apparatus 200 is not limited by the form of thecomputer-readable media on which the instructions for the process arestored. For example, the instructions may be stored on CDs, DVDs, inFLASH memory, RAM, ROM, PROM, EPROM, EEPROM, hard disk, or any otherinformation processing device with which the controller 105communicates, such as a server or other computer. Further, thefunctionality may be provided as a utility application, backgrounddaemon, or component of an operating system, or combination thereof,executing in conjunction with the processor 101 and an operating systemsuch as Microsoft Windows 7, UNIX, Solaris, LINUX, Apple MAC-OS, andother systems known to those skilled in the art.

The hardware elements used in order to achieve the controller 105 may berealized by various circuitry elements known to those skilled in theart. For example, processor 101 may be a Xenon or Core processor fromIntel of America, or an Opteron processor from AMD of America, or may beother processor types that would be recognized by one of ordinary skillin the art. Alternatively, the processor 101 may be implemented on anFPGA, ASIC, PLD, or using discrete logic circuits, as one of ordinaryskill in the art would recognize. Further, processor 101 may beimplemented as multiple processors cooperatively working in parallel toperform the instructions of the inventive processes described above.

The controller 105 in FIG. 5 also includes a device controller 106. Thedevice controller includes one or more chips or expansion cards,connected to and configured to control the switch 160 and the IRtransceiver 130. These may be configured as, for example, serial orparallel port connections, Ethernet connections, or the like, asappropriate for the switch 160 and the IR transceiver 130, respectively.The device controller 106 provides for all communications required,control or data, between the controller 105 and the switch 160 and theIR transceiver 130.

The controller 105 further includes a display controller 108, such as aNVIDIA GeForce GTX or Quadro graphics adaptor from NVIDIA Corporation ofAmerica for interfacing with display 110, such as a Hewlett PackardHPL2445w LCD monitor. A general purpose I/O interface 112 interfaceswith a keyboard and/or mouse 114 as well as a touch screen panel 116 onor separate from display 110. General purpose I/O interface alsoconnects to a variety of peripherals 118 including printers andscanners, such as an OfficeJet or DeskJet from Hewlett Packard.

A sound controller 120 is also provided in the controller 105, such asSound Blaster X-Fi Titanium from Creative, to interface withspeakers/microphone 122, thereby providing sounds and/or music.

The general purpose storage controller 124 connects the storage mediumdisk 104 with communication bus 126, which may be an ISA, EISA, VESA,PCI, or similar, for interconnecting all of the components of thecontroller 105. A description of the general features and functionalityof the display 110, keyboard and/or mouse 114, as well as the displaycontroller 108, storage controller 124, network controller 106, soundcontroller 120, and general purpose I/O interface 112 is omitted hereinfor brevity, as these features are known.

FIG. 6 is a flowchart illustrating an exemplary embodiment of a methodfor measuring a local acceleration of gravity. At step S100, the rod 170marked with the regular alternating pattern of reflective andnon-reflective portions is released from the electromagnet 140 by thecontroller 105 causing the switch 160 to open.

At step S200, the falling rod 170 is continuously illuminated by the IRLED 132 as the rod falls past the IR transceiver 130. The reflectedlight from the falling rod 170 is modulated by the regular alternatingpattern of reflective portions and non-reflective portions on rod 170.At step S300 the pattern of reflected IR light is continuously detectedby the IR photodiode 134.

At step S400, the output circuit 136 generates a two-state output signalcorresponding to a detected illumination state of the IR photodiode 134by reflected IR light. The two-state output signal has a high state anda low state. The high state may take a value of, for example, 5 V, andcorresponds to the IR photodiode detecting IR light emitted by the IRLED 132 and reflected by a reflective portion 171 of the rod 170. Thelow state may take a value of, for example, 0 V, and corresponds to theIR photodiode detecting IR light emitted by the IR LED 132 and incidenton a non-reflective portion 172 of the rod 170.

At step S500, the processor 101 calculates the times of the transitionsin the output signal from the output circuit 136. The processor 101calculates the times of both rising edge transitions and falling edgetransitions. Each transition represents a distance corresponding to theregular interval in the alternating pattern passing at the particulartime of the transition. The transitions may be identified, for example,by a change in voltage of greater than a threshold voltage from one ofthe two state voltage levels. For example, the voltage threshold can beset at 0.1 V. Then, a transition from the low state to the high state isdetermined to be when the voltage increases from 0 V to 0.1 V.Similarly, a transition from the high state to the low state isdetermined to be when the voltage decreases from 5 V to 4.9 V.Alternatively, a more complicated algorithm known to one of ordinaryskill in the art may be used for calculating the times of thetransitions.

This produces a time for each transition. However, from the geometry ofthe regular alternating pattern on the rod 170, a distance between eachtransition is also known. For example, if each reflective portion 171and each non-reflective portion 172 is 1.0 cm in length, then there is1.0 cm between each transition. Combining the characterizations of thetransitions in time and distance, a set of data points including aposition and time for each transition is produced.

At step S600, the processor 101 fits the position and time data pointsdetermined from the transitions to the kinematic equation for a fallingbody. The one dimensional equation of motion under constant accelerationis known to be a second order polynomial in time. Therefore, the y(t)versus t data is fit to a polynomial of second degreey(t)=a ₀ +a ₁ t+a ₂ t ²using an ordinary least squares estimation to determine the values ofthe coefficients a₀, a₁, and a₂.

FIG. 7 illustrates an exemplary curve fit of data to show the localacceleration of gravity in an aspect of the disclosure using ordinaryleast squares estimation. FIG. 6 shows the time of the stripes relativeto the start of ascending of the IR reflected signal of the first whitestripe (choosing the initial data point to be at y₀=t₀=0) versus theelapsed time of fall in seconds. For the rod 170 having 10 reflectiveportions 171 and 9 non-reflective portions 172, the 19 data pointsfollow a quadratic curve.

At step S700, the processor 101 calculates a local acceleration ofgravity g using the coefficients obtained from the fitting at step S600.To extract the value of acceleration due to gravity, we utilize the onedimensional equation of motion under constant acceleration, which iscommonly given asy(t)=y ₀ +v ₀ t+½gt ².By comparing the coefficients of the quadratic fit to the equation ofmotion, it is possible to extract a value of the acceleration due togravity. The acceleration of gravity, g, is calculated as twice thecoefficient a₂ obtained from the fit. This completes the method forcalculating a local acceleration of gravity.

In order to improve the precision and accuracy of the experiment, themethod may be repeated N times, for example, 25 times. This may beaccomplished either by repeating steps S100 through S500 N times and atstep S600 fitting the entire data set of all position and time datapoints from the N repetitions, or by executing steps S100 through S700 Ntimes to calculate N values of g, and then finding the average value gof the N values of g.

While certain embodiments have been described herein, these embodimentsare presented by way of example only, and are not intended to limit thescope of the disclosure. Indeed, using the teachings in this disclosure,a person having ordinary skill in the art could modify and adapt thedisclosure in a various ways, making omissions, substitutions andchanges in the form of the embodiments described herein withoutdeparting from the spirit of the disclosure. Moreover, in interpretingthe disclosure, all terms should be interpreted in the broadest possiblemanner consistent with the context. The accompanying claims and theirequivalents are intended to cover such forms or modifications as wouldfall within the scope and spirit of the disclosure.

For example, the fitting the position and time data points determinedfrom the transitions can also be accomplished by other methods availableto one of ordinary skill in the art, for example, by a weighted leastsquares approach or another linear regression model.

We claim:
 1. An apparatus for measuring a local acceleration of gravity,the apparatus comprising: a ferrous rod having a regular alternatingpattern of reflective and non-reflective portions on a surface thereof;an electromagnetic holder configured to releasably hold the ferrous rod;an infrared (IR) transceiver including a light emitting diode (LED)configured to emit IR light, a photodiode configured to detect IR lightemitted by the LED which is reflected back to the IR transceiver, and anoutput circuit configured to output a two-state signal corresponding toan illumination state of the photodiode by the reflected IR light; apower supply configured to the power the electromagnetic holder and theIR transceiver; and circuitry configured to: control a current from thepower supply to the electromagnetic holder to the cause electromagneticholder to release the rod, cause the IR transceiver to emit IR light,receive the signal from the IR transceiver, calculate times oftransitions between the two states in the received signal to determinekinematic data, and calculate a local acceleration of gravity from a fitto the kinematic data.
 2. The apparatus according to claim 1, whereinthe rod has a substantially cylindrical shape.
 3. The apparatusaccording to claim 1, wherein the alternating pattern is formed atregular intervals of 1 centimeter.
 4. The apparatus according to claim1, where in the alternating pattern is formed by etching a surface ofthe rod.
 5. The apparatus according to claim 1, wherein the alternatingpattern is formed by applying a black resin, epoxy, or paint to asurface of the ferrous rod.
 6. The apparatus according to claim 5,wherein transitions between the reflective portions and thenon-reflective portions of the alternating pattern are blurred byvarying a concentration of an IR absorber in the black resin, epoxy, orpaint in a portion of the alternating pattern at the transition.
 7. Theapparatus according to claim 5, wherein the surface of the rod is shapedin a pattern corresponding to the reflective portions and thenon-reflective portions of the rod.
 8. The apparatus according to claim7, wherein the surface of the rod is shaped in a concave patterncorresponding to the reflective portions and the non-reflective portionsof the rod.
 9. The apparatus according to claim 1, wherein thealternating pattern is formed by printing a black and white pattern onpaper and fixing the paper to the ferrous rod.
 10. A method formeasuring a local acceleration of gravity comprising: releasing aferrous object having a regular alternating pattern of reflective andnon-reflective portions on a surface thereof from an electromagneticholder so that the object falls with a substantially verticalacceleration and substantially no angular velocity about a center ofmass of the object; illuminating the falling object with a lightemitting diode (LED) configured to emit infrared (IR) light; detectingIR light emitted by the LED and reflected by the falling object with aphotodiode configured to detect IR light emitted by the LED andreflected by the falling object; generating a two-state signal based onthe detecting, the two-state signal corresponding to an illuminationstate of the photodiode by the reflected IR light; calculating times oftransitions between the two states in the generated signal to determinekinematic data; fitting the kinematic data to a predetermined curve; andcalculating a local acceleration of gravity from the fitting.
 11. Themethod according to claim 10, further comprising: second releasing theferrous object having the regular alternating pattern of reflective andnon-reflective portions on the surface thereof from the electromagneticholder so that the object falls with a substantially verticalacceleration and substantially no angular velocity about the center ofmass of the object; second illuminating the falling object with a lightemitting diode (LED) configured to emit infrared (IR) light; seconddetecting IR light emitted by the LED and reflected by the fallingobject with a photodiode configured to detect IR light emitted by theLED and reflected by the falling object; second generating a two-statesignal based on the detecting, the two-state signal corresponding to anillumination state of the photodiode by the reflected IR light; andsecond calculating times of transitions between the two states in thegenerated signal to determine kinematic data, wherein the releasing is afirst releasing, wherein the illuminating is a first illuminating,wherein the detecting is a first detecting, wherein the generating is afirst generating, wherein the calculating is a first calculating, andwherein the fitting the kinematic data to the predetermined curveincludes the kinematic data from the first calculating and the kinematicdata from the second calculating.
 12. A non-transitory computer-readablemedium storing a program thereon for causing a computer to perform amethod for measuring a local acceleration of gravity, the methodcomprising: releasing a ferrous object having a regular alternatingpattern of reflective and non-reflective portions on a surface thereoffrom an electromagnetic holder so that the object falls with asubstantially vertical acceleration and substantially no angularvelocity about a center of mass of the object; illuminating the fallingobject with a light emitting diode (LED) configured to emit infrared(IR) light; detecting IR light emitted by the LED and reflected by thefalling object with a photodiode configured to detect IR light emittedby the LED and reflected by the falling object; generating a two-statesignal based on the detecting, the two-state signal corresponding to anillumination state of the photodiode by the reflected IR light;calculating times of transitions between the two states in the generatedsignal to determine kinematic data; fitting the kinematic data to apredetermined curve; and calculating a local acceleration of gravityfrom the fitting.